Calculation method of vertical stiffness of oval cross-section wire diameter truncated cone type helical spring

Abstract

The present invention belongs to the technical field of vertical stiffness calculation of oval cross-section wire diameter type truncated cone type spiral spring, and specifically relates to a method for calculating the vertical stiffness of oval cross-section wire diameter type truncated cone type spiral spring. The present invention can calculate the vertical stiffness of the oval cross-section wire diameter type truncated cone type spiral spring based on the structural parameters and material characteristic parameters of the oval cross-section wire diameter type truncated cone type spiral spring, taking into account the coordinate offset of the center of mass of the oval cross-section. Through ANSYS simulation and experimental verification of the prototype, it can be known that the method can obtain accurate and reliable calculation values ​​of the vertical stiffness of the oval cross-section wire diameter type truncated cone type spiral spring, ensure that the vertical stiffness meets the design requirements, and lay a reliable technical foundation for the design of oval cross-section wire diameter type truncated cone type spiral spring and key parameters, thereby improving the product design level and performance and the stability and safety of vehicle driving; at the same time, it also reduces design and testing costs and speeds up product development.

Description

Technical Field

[0001] The invention relates to a method for calculating the vertical stiffness of an oval-section wire diameter type truncated cone-shaped spiral spring, belonging to the technical field of vertical stiffness calculation of an oval-section wire diameter type truncated cone-shaped spiral spring. Background Art

[0002] With the rapid development of vehicles and the continuous increase in driving speed, higher requirements are placed on the performance and design of vehicle suspension springs. In order to meet the design requirements of stress strength and installation space of spiral springs, oval-section wire diameter type truncated cone type spiral springs are sometimes used. However, since the wire diameter section is an oval section and the middle diameter changes with the polar angle position, the vertical stiffness calculation of the oval-section wire diameter type truncated cone type spiral spring is very complicated. According to the information found, at present, no accurate and reliable calculation method for the vertical stiffness of oval-section wire diameter type truncated cone type spiral springs has been given at home and abroad. With the continuous increase in vehicle driving speed and the requirements for driving stability and safety, higher requirements are placed on the design of vehicle suspension springs, which must meet the design requirements of spiral spring installation and vertical stiffness. Therefore, it is necessary to establish an accurate and reliable method for calculating the vertical stiffness of the oval-section wire diameter truncated cone-shaped coil spring, so as to lay a reliable technical foundation for the design of the oval-section wire diameter truncated cone-shaped coil spring and its key parameters, thereby improving the product's forward development design capability, design level, reliability and service life, and meeting the requirements of vehicle ride smoothness and safety; at the same time, reducing product design and testing costs and speeding up product development. Summary of the invention

[0003] In view of the above shortcomings in the prior art, the object of the present invention is to provide a method for calculating the vertical stiffness of an oval cross-section wire diameter type truncated cone type helical spring, which can accurately and reliably calculate the vertical stiffness of an oval cross-section wire diameter type truncated cone type helical spring. The calculation flow chart is as follows: Figure 1 shown.

[0004] The calculation method of the vertical stiffness of the oval cross-section wire diameter type truncated cone type spiral spring of the present invention, the schematic diagram of the wire diameter oval cross-section of the oval cross-section wire diameter type truncated cone type spiral spring, as shown in FIG. Figure 2 As shown, the oval section can be regarded as a combination of half an ellipse and half a circle. The radius of the semicircle is equal to the short semi-axis of the ellipse, that is, the long semi-axis b of the oval section. The short semi-axis of the oval section is a, o is the center of the semicircle, ox is the center of mass of the oval section, and the coordinate system of the wire diameter oval section is established with the center of mass ox of the oval section as the coordinate origin, where x0 is the coordinate offset of the center of mass of the oval section, D1 and D2 are the median diameters of the semicircle center of the oval section at the beginning and end of the truncated cone type coil spring, that is, the beginning median diameter D1 and the end median diameter D2. The schematic diagram of the structure and parameter symbols of the oval section wire diameter truncated cone type coil spring is as follows, Figure 3As shown, the center of the first end of the truncated cone coil spring is the origin O, the effective starting point of the origin O to the wire diameter is the X-axis, and the center of the middle diameter of the end is the Z-axis. The effective height H0 of the coil spring and the rise angle α are respectively D1x and D2x, which are the effective middle diameter D1x and D2x of the first end of the truncated cone coil spring under the consideration of the cross-section centroid coordinate offset x0. The elastic modulus E, Poisson's ratio μ, and shear modulus G of the coil spring. According to the structural parameters, elastic modulus, Poisson's ratio, and shear modulus of the oval cross-section wire diameter truncated cone coil spring, the vertical stiffness of the oval cross-section wire diameter truncated cone coil spring is calculated to ensure that the vertical stiffness of the oval cross-section wire diameter truncated cone coil spring meets the design requirements of the vehicle suspension.

[0005] In order to solve the above technical problems, the present invention provides a method for calculating the vertical stiffness of an oval cross-section wire diameter type truncated cone type spiral spring, which adopts the following calculation steps:

[0006] (1) Calculation of the rise angle α of the oval cross-section wire diameter truncated cone type helical spring:

[0007] According to the effective number of coils n, effective height H0, the middle diameter D1 of the first end and the middle diameter D2 of the oval cross-section wire diameter truncated cone type spiral spring, the rise angle α of the oval cross-section wire diameter truncated cone type spiral spring is calculated, that is,

[0008]

[0009] Where LC is the total arc length of the n-turn wire diameter in the horizontal projection plane,

[0010] (2) Calculation of the centroid coordinate offset x0 of the oval cross section of the coil spring wire diameter:

[0011] According to the major semi-axis b and minor semi-axis a of the oval section of the wire diameter, the centroid coordinate offset x0 of the oval section of the wire diameter is calculated, that is,

[0012]

[0013] (3) Calculation of the moment of inertia Ib and polar moment of inertia Ip of the oval cross section of the helical spring wire diameter:

[0014] According to the major semi-axis b, minor semi-axis a of the wire diameter oval section, and x0 calculated in step (2), the moment of inertia Ib and polar moment of inertia Ip of the wire diameter oval section are calculated, namely:

[0015]

[0016]

[0017] (4) Calculation of vertical flexibility Rdz of oval cross-section wire diameter truncated cone type helical spring:

[0018] Step I: Calculation of the effective median diameters D1x and D2x at the beginning and end of an oval-section wire-diameter truncated cone-shaped helical spring

[0019] According to the middle diameter D1 of the head end and the middle diameter D2 of the end of the oval cross-section wire diameter type truncated cone type coil spring, and the centroid coordinate offset x0 of the oval cross-section calculated in step (2), the effective middle diameters D1x and D2x of the head end and the end of the oval cross-section wire diameter type truncated cone type coil spring under the consideration of the centroid coordinate offset x0 of the cross-section are calculated, that is, D1x = D1-2x0,

[0020] D2x=D2-2x0.

[0021] Step II: Calculation of the vertical flexibility Rdz of the oval cross-section wire diameter truncated cone type helical spring

[0022] According to the effective number of coils n of the oval-section wire diameter type truncated cone type coil spring, the elastic modulus E, the shear modulus G, the α calculated in step (1), the x0 calculated in step (2), the Ib and Ip calculated in step (3), and the D1x and D2x calculated in step I, the vertical flexibility Rdz of the oval-section wire diameter type truncated cone type coil spring is calculated, that is,

[0023]

[0024] (5) Calculation of the vertical stiffness Kz of the oval cross-section wire diameter truncated cone type helical spring:

[0025] According to the Rdz calculated in step (4), the vertical stiffness Kz of the oval-section wire diameter truncated cone-shaped helical spring is calculated, namely:

[0026]

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] The method for calculating the vertical stiffness of the oval-section wire diameter type truncated cone-shaped coil spring of the present invention can calculate the vertical stiffness of the oval-section wire diameter type truncated cone-shaped coil spring according to the structural parameters and material characteristic parameters of the oval-section wire diameter type truncated cone-shaped coil spring, that is, according to the major semi-axis and minor semi-axis of the oval wire diameter section, the effective number of turns, the effective height, the middle diameter of the first end and the middle diameter of the last end of the truncated cone-shaped coil spring, the elastic modulus, Poisson's ratio and shear modulus of the coil spring material, while considering the centroid coordinate offset of the oval wire diameter section; through ANSYS simulation and experimental verification of the prototype, it can be known that the method can obtain an accurate and reliable calculation value of the vertical stiffness of the oval-section wire diameter type truncated cone-shaped coil spring, ensure that the vertical stiffness of the oval-section wire diameter type truncated cone-shaped coil spring meets the design requirements, can improve the product's forward development design capability, design level and performance, and improve the vehicle's driving smoothness; at the same time, it also reduces design and testing costs and speeds up product development. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 It is a flow chart for calculating the vertical stiffness of an oval cross-section wire diameter truncated cone type helical spring;

[0030] Figure 2 It is a schematic diagram of the oval cross section of the oval cross section wire diameter type truncated cone type helical spring wire diameter;

[0031] Figure 3 It is a schematic diagram of the structure and parameter symbols of an oval-section wire diameter truncated cone-shaped helical spring. DETAILED DESCRIPTION

[0032] The embodiments of the present invention are further described below in conjunction with the accompanying drawings:

[0033] Embodiment 1:

[0034] like Figures 1 to 3 As shown in the figure, a suspension spring adopts an oval cross-section wire diameter truncated cone type spiral spring to meet the installation requirements. Among them, the middle diameter of the truncated cone type spiral spring is D1 = 100mm at the head end, D2 = 130mm at the end, the long semi-axis b = 7.0mm, the short semi-axis a = 5.5mm, the effective number of turns n = 4.5, the effective height H0 = 350mm, the elastic modulus E = 206GPa, the Poisson's ratio μ = 0.3, and the shear modulus According to the structural parameters, elastic modulus, Poisson's ratio and shear modulus of the oval cross-section wire diameter type truncated cone type spiral spring, the vertical stiffness of the oval cross-section wire diameter type truncated cone type spiral spring is calculated.

[0035] The calculation method of the vertical stiffness of the oval cross-section wire diameter type truncated cone type spiral spring provided by the embodiment of the present invention has the following calculation process: Figure 1 As shown, the specific calculation steps are as follows:

[0036] (1) Calculation of the rise angle α of the oval cross-section wire diameter truncated cone type helical spring:

[0037] According to the effective number of coils n = 4.5, effective height H0 = 350mm, the middle diameter D1 = 100mm and the middle diameter D2 = 130mm of the oval cross-section wire diameter truncated cone type coil spring, the rise angle α of the oval cross-section wire diameter truncated cone type coil spring is calculated, that is,

[0038]

[0039] Where, L C is the total arc length of n wire circles in the horizontal projection plane,

[0040] (2) Calculation of the centroid coordinate offset x0 of the oval cross section of the coil spring wire diameter:

[0041] According to the long semi-axis b = 7.0 mm and the short semi-axis a = 5.5 mm of the oval section of the wire diameter, the centroid coordinate offset x0 of the oval section of the wire diameter is calculated, that is,

[0042]

[0043] (3) Moment of inertia I of the oval cross section of the helical spring wire b and polar moment of inertia I p Calculation:

[0044] According to the long semi-axis b = 7.0 mm, the short semi-axis a = 5.5 mm of the wire diameter oval section, and the x0 = 0.6366 mm calculated in step (2), the moment of inertia I of the wire diameter oval section is b and polar moment of inertia I p Calculate, that is

[0045]

[0046]

[0047] (4) Vertical flexibility R of oval cross-section wire diameter truncated cone type helical spring dz Calculation:

[0048] Step I: The effective mid-diameter D of the first and last ends of the oval cross-section wire diameter truncated cone type coil spring 1x and D 2x Calculation

[0049] According to the oval cross-section wire diameter truncated cone type spiral spring D1 = 100mm, the end median diameter D2 = 130mm, and the oval cross-section centroid coordinate offset x0 = 0.6366mm calculated in step (2), the effective median diameter D of the head and end of the oval cross-section wire diameter truncated cone type spiral spring considering the cross-section centroid coordinate offset x0 is 1x and D 2x Calculate, that is

[0050] D 1x =D1-2x0=98.7mm,

[0051] D 2x =D2-2x0=128.7mm.

[0052] Step II: Vertical flexibility R of oval cross-section wire diameter truncated cone type coil spring dz Calculation

[0053] According to the effective number of coils n of the oval-section wire diameter truncated cone-shaped coil spring = 4.5, the elastic modulus E of the coil spring material = 206 GPa, the shear modulus G = 79.231 GPa, the α calculated in step (1) = 12.1493°, the x0 calculated in step (2) = 0.6366 mm, and the I calculated in step (3) b =1.0564×10 3 mm 4 and I p =1.8731×10 3 mm 4 , and D calculated in step I 1x =98.7mm and D 2x =128.7mm, vertical flexibility R of oval cross-section wire diameter truncated cone type coil spring dz Calculate, that is

[0054]

[0055] (5) Vertical stiffness K of oval cross-section wire diameter truncated cone type helical spring z Calculation:

[0056] According to the R calculated in step (4) dz =3.5942×10 -2 mm / N, vertical stiffness K of oval cross-section wire diameter truncated cone type helical spring z Calculate, that is

[0057]

[0058] Through ANSYS simulation and experimental testing of the prototype, it can be known that the calculation method of the vertical stiffness of the oval-section wire diameter truncated cone-shaped coil spring provided by the present invention is correct, and can obtain accurate and reliable calculation values ​​of the vertical stiffness of the oval-section wire diameter truncated cone-shaped coil spring, which lays a reliable technical foundation for the design of the oval-section wire diameter truncated cone-shaped coil spring and its key parameters for vehicle suspension, ensuring that the vertical stiffness meets the design requirements of the vehicle suspension. The method can improve the forward development and design capabilities of the coil spring, improve the product design level, product quality, and vehicle driving smoothness and safety; at the same time, it can also reduce product design and testing costs and speed up product development.

Claims

1. A method for calculating the vertical stiffness of an oval cross-section wire diameter truncated cone type helical spring, wherein: The cross section of the wire diameter is oval, which can be regarded as composed of half a circle and half an ellipse, and the middle diameter of the first end of the coil spring is not equal to the middle diameter of the end, that is, an oval cross-section wire diameter type truncated cone type coil spring; according to the structural parameters and material characteristic parameters of the oval cross-section wire diameter type truncated cone type coil spring, the vertical stiffness of the oval cross-section wire diameter type truncated cone type coil spring is calculated, which is characterized in that the calculation steps are as follows: (1) Calculation of the rise angle α of the oval cross-section wire diameter truncated cone type helical spring: According to the effective number of coils n, effective height H0, the middle diameter D1 of the first end and the middle diameter D2 of the oval cross-section wire diameter truncated cone type spiral spring, the rise angle α of the oval cross-section wire diameter truncated cone type spiral spring is calculated, that is, Where, L C is the total arc length of n wire circles in the horizontal projection plane, (2) Calculation of the centroid coordinate offset x0 of the oval cross section of the coil spring wire diameter: According to the major semi-axis b and minor semi-axis a of the oval section of the wire diameter, the centroid coordinate offset x0 of the oval section of the wire diameter is calculated, that is, (3) Moment of inertia I of the oval cross section of the helical spring wire b and polar moment of inertia I p Calculation: According to the major semi-axis b and minor semi-axis a of the wire diameter oval section, and the x0 calculated in step (2), the moment of inertia I of the wire diameter oval section is b and polar moment of inertia I p Calculate, that is (4) Vertical flexibility R of oval cross-section wire diameter truncated cone type helical spring dz Calculation: Step I: The effective median diameter D of the first and last ends of the oval cross-section wire diameter truncated cone type coil spring 1x and D 2x Calculation According to the middle diameter D1 of the head end and the middle diameter D2 of the end of the oval cross-section wire diameter type truncated cone type spiral spring, and the centroid coordinate offset x0 of the oval cross-section calculated in step (2), the effective middle diameter D1 of the head end and the end of the oval cross-section wire diameter type truncated cone type spiral spring under the consideration of the centroid coordinate offset x0 of the cross-section is calculated. 1x and D 2x Calculate, that is D 1x =D1-2x0, D 2x =D2-2x0; Step II: Vertical flexibility R of oval cross-section wire diameter truncated cone type coil spring dz Calculation According to the effective number of coils n, elastic modulus E, shear modulus G of the oval cross-section wire diameter truncated cone type coil spring, α calculated in step (1), x0 calculated in step (2), I calculated in step (3) b and I p , and D calculated in step I 1x and D 2x , the vertical flexibility R of the oval cross-section wire diameter truncated cone type coil spring dz Calculate, that is (5) Vertical stiffness K of oval cross-section wire diameter truncated cone type helical spring z Calculation: According to the R calculated in step (4) dz , the vertical stiffness K of the oval cross-section wire diameter truncated cone type helical spring z Calculate, that is

Images